How can you find the density with bathtub and weight scale?
Easiest way: Weigh the object in air then weigh the object submerged in the water and use the equation of bouyancy to determine the density relative to water (which you already know the density of). Bingo. Even if the object floats the principle still works, but then you have to measure the objects bouyency with the scale (turn the scale upside down in the water and measure the pull required to sink it). No need to measure the water volume change (which your statement apparently does not allow). This method also eliminates the variation of g due to being on a mountain or on the moon or wherever. No need to spill water, lol.
